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Numerical Solution of the Hamilton-Jacobi-Bellman Equation in Stochastic Optimal Control with Application of Portfolio Optimization


H. Peyrl

International Conference of Computational Methods in Sciences and Engineering

This paper provides a numerical solution of the Hamilton-Jacobi-Bellman (HJB) equation for stochastic optimal control problems. The computation's difficulty is due to the nature of the HJB equation being a second-order partial differential equation which is coupled with an optimization. By using a successive approximation algorithm, the optimization gets separated from the boundary value problem. This makes the problem solvable by standard numerical methods. The method's usefulness is shown in an example of portfolio optimization with no known analytical solution.


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